What Is the Circle Area Calculator?
This calculator finds the area of a circle from its radius using the classic formula \(A = \pi r^{2}\). A circle is the set of all points equidistant from a center point, and that distance is the radius (r). Knowing the area is useful for everything from designing round tables and pizzas to engineering pipes, gardens, and landscaping projects.
How to Use It
Enter the radius of your circle in any unit you like (centimeters, meters, inches, feet). The calculator returns the area in those units squared, along with the diameter (2r) and circumference (2πr) for convenience. If you only know the diameter, simply divide it by two to get the radius first.
The Formula Explained
The area formula is $$A = \pi \times r^{2}$$, where \(\pi\) (pi) \(\approx 3.14159\) and \(r\) is the radius. The radius is squared because area is a two-dimensional measure that grows with the square of any linear scaling. Double the radius and the area quadruples. The circumference uses \(C = 2\pi r\), a linear measure of the distance around the circle.
Worked Example
Suppose a circle has a radius of 5 units. Then $$A = \pi \times 5^{2} = \pi \times 25 \approx 78.54 \text{ square units}.$$ Its diameter is \(2 \times 5 = 10\) units and its circumference is \(2 \times \pi \times 5 \approx 31.42\) units.
FAQ
What if I only know the diameter? Divide the diameter by 2 to get the radius, then enter it. For example, a diameter of 10 means a radius of 5.
Does the unit matter? No — the result is simply in whatever unit you used, squared. Inches give square inches, meters give square meters.
How accurate is pi here? The calculator uses the full double-precision value of \(\pi\), so results are accurate to many decimal places.
